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SUMMARY:Two-point function of O(n) models below the critical dimension
DTSTART;VALUE=DATE-TIME:20171122T153000Z
DTEND;VALUE=DATE-TIME:20171122T163000Z
DTSTAMP;VALUE=DATE-TIME:20191118T170023Z
UID:indico-event-2964@indico.math.cnrs.fr
DESCRIPTION:We will discuss the asymptotic behaviour of the critical two-p
oint function for a long-range version of the n-component $|varphi|^4$ mod
el and the weakly self-avoiding walk (WSAW) on the d-dimensional Euclidean
lattice with d=1\,2\,3. The WSAW corresponds to the case n=0 via a supers
ymmetric integral representation. We choose the range of the interaction s
o that the upper-critical dimension of both models is $d+epsilon$. Our mai
n result is that\, for small $epsilon$ and small coupling strength\, the c
ritical two-point function exhibits mean-field decay\, confirming a predic
tion of Fisher\, Ma\, and Nickel. The proof makes use of a renormalisation
group method of Bauerschmidt\, Brydges\, and Slade\, as well as a cluster
expansion. This is joint work with Martin Lohmann and Gordon Slade.\n\nht
tps://indico.math.cnrs.fr/event/2964/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/2964/
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